I already corrected as -ebilmek and -abilmek. 

Now please check below from the site http://www.edebiyatogretmeni.net/fiiller.htm

It is called Yeterlilik Fiili, because it is a verb..

1) Yeterlilik Fiili ( fiil + ebil-) :

Cümleye gücü yetme ve olasýlýk anlamý katar.Fiilin üzerine ebilmek getirilerek oluþturulur.

* Okula geç kalýrsam öðretmenim kýzabilir. (o)

* Bu genç yaþýmda ölebilirim (o)

*En güzel þiirlerimi söylemeden gidebilirim buralardan (o)

* Bir gece ansýzýn gelebilirim. (o)

* Sevinçten kapýnda bayýlabilirim.

* Sýnýfý geçebilirim (g.y)

UYARI: Yeterlilik fiilinin olumsuzunda bil- fiili düþer. Fiilin üzerine –ama , -eme getirilerek yapýlýr.

* Yapabilirim à yapamam. (yeterlilik birleþik fiilinin olumsuzu)

* yaparým    à   yapmam  ( geniþ zamanýn olumsuzu)  

* Görebilirsin à göremezsin (yeterlilik birleþik fiilinin olumsuzu)

* Atamam kendimi mavi denize dünya güzel. (atabilirim: yeterlilik birleþik fiilinin olumsuzu)

 Thats merely what I am saying It is not correct for turkish grammar, even if itd be the origine. And the gidebilmem I gave, was not intended as Azeri Turkish example, it was intended as an example why it would be inconsequent to view the ability-suffix as a verb.

 I didnt see you corrected it, sorry.

And I know of the type of source you gave. But Turkish ´dil bilgisi / bilimi´ is mainly based upon west-european linguistical concepts that do not fit Turkish language. That is why it is so interesting to discuss about Turkish grammar rules and how they should be named

 And welcome to the site, (thehandsom! did you do your duty as welcomer??), I have been away for quite some time and I havent noticed you around before. Hope you enjoy our website!

Thank you and yes, I enjoy the website..